Conformally flat generalized Sasakian-space-forms and locally symmetric generalized Sasakian-space-forms. (English) Zbl 1118.53025

P. Alegre, D. E. Blair and A. Carriazo [Isr. J. Math. 141, 157–183 (2004; Zbl 1064.53026)] introduced the so-called generalized Sasakian-space forms. Such spaces are almost contact metric manifolds whose curvature tensor has a special expression. In the present paper, the author classifies generalized Sasakian-space forms under the additional assumption that they are conformally flat and the characteristic vector field is Killing. Moreover, he classifies locally symmetric generalized Sasakian-space forms.
Reviewer: D. Perrone (Lecce)


53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
53D15 Almost contact and almost symplectic manifolds


Zbl 1064.53026